Describes a branch of a hyperbola in 3D space. A hyperbola is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where: More...

#include <Geom_Hyperbola.hxx>

Inheritance diagram for Geom_Hyperbola:

[legend]

Public Member Functions
	Geom_Hyperbola (const gp_Hypr &H)
	Constructs a hyperbola by conversion of the gp_Hypr hyperbola H.

	Geom_Hyperbola (const gp_Ax2 &A2, const Standard_Real MajorRadius, const Standard_Real MinorRadius)
	Constructs a hyperbola defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the hyperbola and defines its orientation in 3D space such that:

void	SetHypr (const gp_Hypr &H)
	Converts the gp_Hypr hyperbola H into this hyperbola.

void	SetMajorRadius (const Standard_Real MajorRadius)
	Assigns a value to the major radius of this hyperbola. Exceptions Standard_ConstructionError if:

void	SetMinorRadius (const Standard_Real MinorRadius)
	Assigns a value to the minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

gp_Hypr	Hypr () const
	returns the non transient parabola from gp with the same geometric properties as <me>.

Standard_Real	ReversedParameter (const Standard_Real U) const override
	Computes the parameter on the reversed hyperbola, for the point of parameter U on this hyperbola. For a hyperbola, the returned value is: -U.

Standard_Real	FirstParameter () const override
	Returns RealFirst from Standard.

Standard_Real	LastParameter () const override
	returns RealLast from Standard.

Standard_Boolean	IsClosed () const override
	Returns False.

Standard_Boolean	IsPeriodic () const override
	return False for an hyperbola.

gp_Ax1	Asymptote1 () const
	In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = (B/A)*X. Raises ConstructionError if MajorRadius = 0.0.

gp_Ax1	Asymptote2 () const
	In the local coordinate system of the hyperbola the equation of the hyperbola is (XX)/(AA) - (YY)/(BB) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X. Raises ConstructionError if MajorRadius = 0.0.

gp_Hypr	ConjugateBranch1 () const
	This branch of hyperbola is on the positive side of the YAxis of <me>.

gp_Hypr	ConjugateBranch2 () const
	This branch of hyperbola is on the negative side of the YAxis of <me>. Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola.

gp_Ax1	Directrix1 () const
	This directrix is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the YAxis. The intersection point between directrix1 and the XAxis is the location point of the directrix1. This point is on the positive side of the XAxis.

gp_Ax1	Directrix2 () const
	This line is obtained by the symmetrical transformation of "directrix1" with respect to the YAxis of the hyperbola.

Standard_Real	Eccentricity () const override
	Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. raised if MajorRadius = 0.0.

Standard_Real	Focal () const
	Computes the focal distance. It is the distance between the two focus of the hyperbola.

gp_Pnt	Focus1 () const
	Returns the first focus of the hyperbola. This focus is on the positive side of the XAxis of the hyperbola.

gp_Pnt	Focus2 () const
	Returns the second focus of the hyperbola. This focus is on the negative side of the XAxis of the hyperbola.

Standard_Real	MajorRadius () const
	Returns the major or minor radius of this hyperbola. The major radius is also the distance between the center of the hyperbola and the apex of the main branch (located on the "X Axis" of the hyperbola).

Standard_Real	MinorRadius () const
	Returns the major or minor radius of this hyperbola. The minor radius is also the distance between the center of the hyperbola and the apex of a conjugate branch (located on the "Y Axis" of the hyperbola).

gp_Hypr	OtherBranch () const
	Computes the "other" branch of this hyperbola. This is the symmetrical branch with respect to the center of this hyperbola. Note: The diagram given under the class purpose indicates where the "other" branch is positioned in relation to this branch of the hyperbola.

Standard_Real	Parameter () const
	Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. raised if MajorRadius = 0.0.

void	D0 (const Standard_Real U, gp_Pnt &P) const override
	Returns in P the point of parameter U. P = C + MajorRadius * Cosh (U) * XDir + MinorRadius * Sinh (U) * YDir where C is the center of the hyperbola , XDir the XDirection and YDir the YDirection of the hyperbola's local coordinate system.

void	D1 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1) const override
	Returns the point P of parameter U and the first derivative V1.

void	D2 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2) const override
	Returns the point P of parameter U, the first and second derivatives V1 and V2.

void	D3 (const Standard_Real U, gp_Pnt &P, gp_Vec &V1, gp_Vec &V2, gp_Vec &V3) const override
	Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

gp_Vec	DN (const Standard_Real U, const Standard_Integer N) const override
	The returned vector gives the value of the derivative for the order of derivation N. Raised if N < 1.

void	Transform (const gp_Trsf &T) override
	Applies the transformation T to this hyperbola.

Handle< Geom_Geometry >	Copy () const override
	Creates a new object which is a copy of this hyperbola.

virtual void	DumpJson (Standard_OStream &theOStream, Standard_Integer theDepth=-1) const override
	Dumps the content of me into the stream.

Public Member Functions inherited from Geom_Conic
void	SetAxis (const gp_Ax1 &theA1)
	Changes the orientation of the conic's plane. The normal axis to the plane is A1. The XAxis and the YAxis are recomputed.

void	SetLocation (const gp_Pnt &theP)
	changes the location point of the conic.

void	SetPosition (const gp_Ax2 &theA2)
	changes the local coordinate system of the conic.

const gp_Ax1 &	Axis () const
	Returns the "main Axis" of this conic. This axis is normal to the plane of the conic.

const gp_Pnt &	Location () const
	Returns the location point of the conic. For the circle, the ellipse and the hyperbola it is the center of the conic. For the parabola it is the Apex of the parabola.

const gp_Ax2 &	Position () const
	Returns the local coordinates system of the conic. The main direction of the Axis2Placement is normal to the plane of the conic. The X direction of the Axis2placement is in the plane of the conic and corresponds to the origin for the conic's parametric value u.

gp_Ax1	XAxis () const
	Returns the XAxis of the conic. This axis defines the origin of parametrization of the conic. This axis is perpendicular to the Axis of the conic. This axis and the Yaxis define the plane of the conic.

gp_Ax1	YAxis () const
	Returns the YAxis of the conic. The YAxis is perpendicular to the Xaxis. This axis and the Xaxis define the plane of the conic.

void	Reverse () override
	Reverses the direction of parameterization of <me>. The local coordinate system of the conic is modified.

GeomAbs_Shape	Continuity () const override
	The continuity of the conic is Cn.

Standard_Boolean	IsCN (const Standard_Integer N) const override
	Returns True. Raised if N < 0.

Public Member Functions inherited from Geom_Curve
virtual Standard_Real	TransformedParameter (const Standard_Real U, const gp_Trsf &T) const
	Returns the parameter on the transformed curve for the transform of the point of parameter U on <me>.

virtual Standard_Real	ParametricTransformation (const gp_Trsf &T) const
	Returns a coefficient to compute the parameter on the transformed curve for the transform of the point on <me>.

Handle< Geom_Curve >	Reversed () const
	Returns a copy of <me> reversed.

virtual Standard_Real	Period () const
	Returns the period of this curve. Exceptions Standard_NoSuchObject if this curve is not periodic.

gp_Pnt	Value (const Standard_Real U) const
	Computes the point of parameter U on <me>. If the curve is periodic then the returned point is P(U) with U = Ustart + (U - Uend) where Ustart and Uend are the parametric bounds of the curve. it is implemented with D0.

Public Member Functions inherited from Geom_Geometry
void	Mirror (const gp_Pnt &P)
	Performs the symmetrical transformation of a Geometry with respect to the point P which is the center of the symmetry.

void	Mirror (const gp_Ax1 &A1)
	Performs the symmetrical transformation of a Geometry with respect to an axis placement which is the axis of the symmetry.

void	Mirror (const gp_Ax2 &A2)
	Performs the symmetrical transformation of a Geometry with respect to a plane. The axis placement A2 locates the plane of the symmetry : (Location, XDirection, YDirection).

void	Rotate (const gp_Ax1 &A1, const Standard_Real Ang)
	Rotates a Geometry. A1 is the axis of the rotation. Ang is the angular value of the rotation in radians.

void	Scale (const gp_Pnt &P, const Standard_Real S)
	Scales a Geometry. S is the scaling value.

void	Translate (const gp_Vec &V)
	Translates a Geometry. V is the vector of the translation.

void	Translate (const gp_Pnt &P1, const gp_Pnt &P2)
	Translates a Geometry from the point P1 to the point P2.

Handle< Geom_Geometry >	Mirrored (const gp_Pnt &P) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax1 &A1) const

Handle< Geom_Geometry >	Mirrored (const gp_Ax2 &A2) const

Handle< Geom_Geometry >	Rotated (const gp_Ax1 &A1, const Standard_Real Ang) const

Handle< Geom_Geometry >	Scaled (const gp_Pnt &P, const Standard_Real S) const

Handle< Geom_Geometry >	Transformed (const gp_Trsf &T) const

Handle< Geom_Geometry >	Translated (const gp_Vec &V) const

Handle< Geom_Geometry >	Translated (const gp_Pnt &P1, const gp_Pnt &P2) const

Public Member Functions inherited from Standard_Transient
	Standard_Transient ()
	Empty constructor.

	Standard_Transient (const Standard_Transient &)
	Copy constructor – does nothing.

Standard_Transient &	operator= (const Standard_Transient &)
	Assignment operator, needed to avoid copying reference counter.

virtual	~Standard_Transient ()
	Destructor must be virtual.

virtual const opencascade::handle< Standard_Type > &	DynamicType () const
	Returns a type descriptor about this object.

Standard_Boolean	IsInstance (const opencascade::handle< Standard_Type > &theType) const
	Returns a true value if this is an instance of Type.

Standard_Boolean	IsInstance (const Standard_CString theTypeName) const
	Returns a true value if this is an instance of TypeName.

Standard_Boolean	IsKind (const opencascade::handle< Standard_Type > &theType) const
	Returns true if this is an instance of Type or an instance of any class that inherits from Type. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Boolean	IsKind (const Standard_CString theTypeName) const
	Returns true if this is an instance of TypeName or an instance of any class that inherits from TypeName. Note that multiple inheritance is not supported by OCCT RTTI mechanism.

Standard_Transient *	This () const
	Returns non-const pointer to this object (like const_cast). For protection against creating handle to objects allocated in stack or call from constructor, it will raise exception Standard_ProgramError if reference counter is zero.

Standard_Integer	GetRefCount () const noexcept
	Get the reference counter of this object.

void	IncrementRefCounter () noexcept
	Increments the reference counter of this object.

Standard_Integer	DecrementRefCounter () noexcept
	Decrements the reference counter of this object; returns the decremented value.

virtual void	Delete () const
	Memory deallocator for transient classes.

Additional Inherited Members
Public Types inherited from Standard_Transient
typedef void	base_type
	Returns a type descriptor about this object.

Static Public Member Functions inherited from Standard_Transient
static constexpr const char *	get_type_name ()
	Returns a type descriptor about this object.

static const opencascade::handle< Standard_Type > &	get_type_descriptor ()
	Returns type descriptor of Standard_Transient class.

Protected Attributes inherited from Geom_Conic
gp_Ax2	pos

Detailed Description

Describes a branch of a hyperbola in 3D space. A hyperbola is defined by its major and minor radii and, as with any conic curve, is positioned in space with a right-handed coordinate system (gp_Ax2 object) where:

the origin is the center of the hyperbola,
the "X Direction" defines the major axis, and
the "Y Direction" defines the minor axis. The origin, "X Direction" and "Y Direction" of this coordinate system define the plane of the hyperbola. The coordinate system is the local coordinate system of the hyperbola. The branch of the hyperbola described is the one located on the positive side of the major axis. The "main Direction" of the local coordinate system is a vector normal to the plane of the hyperbola. The axis, of which the origin and unit vector are respectively the origin and "main Direction" of the local coordinate system, is termed the "Axis" or "main Axis" of the hyperbola. The "main Direction" of the local coordinate system gives an explicit orientation to the hyperbola, determining the direction in which the parameter increases along the hyperbola. The Geom_Hyperbola hyperbola is parameterized as follows: P(U) = O + MajRad*Cosh(U)*XDir + MinRad*Sinh(U)*YDir, where:
P is the point of parameter U,
O, XDir and YDir are respectively the origin, "X Direction" and "Y Direction" of its local coordinate system,
MajRad and MinRad are the major and minor radii of the hyperbola. The "X Axis" of the local coordinate system therefore defines the origin of the parameter of the hyperbola. The parameter range is ] -infinite, +infinite [. The following diagram illustrates the respective positions, in the plane of the hyperbola, of the three branches of hyperbolas constructed using the functions OtherBranch, ConjugateBranch1 and ConjugateBranch2: Defines the main branch of an hyperbola. ^YAxis | FirstConjugateBranch | Other | Main ------------------— C ---------------------------—>XAxis Branch | Branch | SecondConjugateBranch | Warning The value of the major radius (on the major axis) can be less than the value of the minor radius (on the minor axis).

Constructor & Destructor Documentation

◆ Geom_Hyperbola() [1/2]

Geom_Hyperbola::Geom_Hyperbola ( const gp_Hypr & H )

Constructs a hyperbola by conversion of the gp_Hypr hyperbola H.

◆ Geom_Hyperbola() [2/2]

Geom_Hyperbola::Geom_Hyperbola	(	const gp_Ax2 &	A2,
		const Standard_Real	MajorRadius,
		const Standard_Real	MinorRadius
	)

Constructs a hyperbola defined by its major and minor radii, MajorRadius and MinorRadius, where A2 locates the hyperbola and defines its orientation in 3D space such that:

the center of the hyperbola is the origin of A2,
the "X Direction" of A2 defines the major axis of the hyperbola, i.e. the major radius MajorRadius is measured along this axis,
the "Y Direction" of A2 defines the minor axis of the hyperbola, i.e. the minor radius MinorRadius is measured along this axis,
A2 is the local coordinate system of the hyperbola. Exceptions Standard_ConstructionError if:
MajorRadius is less than 0.0,
MinorRadius is less than 0.0.

Member Function Documentation

◆ Asymptote1()

gp_Ax1 Geom_Hyperbola::Asymptote1 ( ) const

In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = (B/A)*X. Raises ConstructionError if MajorRadius = 0.0.

◆ Asymptote2()

gp_Ax1 Geom_Hyperbola::Asymptote2 ( ) const

In the local coordinate system of the hyperbola the equation of the hyperbola is (X*X)/(A*A) - (Y*Y)/(B*B) = 1.0 and the equation of the first asymptote is Y = -(B/A)*X. Raises ConstructionError if MajorRadius = 0.0.

◆ ConjugateBranch1()

gp_Hypr Geom_Hyperbola::ConjugateBranch1 ( ) const

This branch of hyperbola is on the positive side of the YAxis of <me>.

◆ ConjugateBranch2()

gp_Hypr Geom_Hyperbola::ConjugateBranch2 ( ) const

This branch of hyperbola is on the negative side of the YAxis of <me>. Note: The diagram given under the class purpose indicates where these two branches of hyperbola are positioned in relation to this branch of hyperbola.

◆ Copy()

Handle< Geom_Geometry > Geom_Hyperbola::Copy ( ) const

overridevirtual

Creates a new object which is a copy of this hyperbola.

Implements Geom_Geometry.

◆ D0()

void Geom_Hyperbola::D0	(	const Standard_Real	U,
		gp_Pnt &	P
	)		const

overridevirtual

Returns in P the point of parameter U. P = C + MajorRadius * Cosh (U) * XDir + MinorRadius * Sinh (U) * YDir where C is the center of the hyperbola , XDir the XDirection and YDir the YDirection of the hyperbola's local coordinate system.

Implements Geom_Curve.

◆ D1()

void Geom_Hyperbola::D1	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1
	)		const

overridevirtual

Returns the point P of parameter U and the first derivative V1.

Implements Geom_Curve.

◆ D2()

void Geom_Hyperbola::D2	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2
	)		const

overridevirtual

Returns the point P of parameter U, the first and second derivatives V1 and V2.

Implements Geom_Curve.

◆ D3()

void Geom_Hyperbola::D3	(	const Standard_Real	U,
		gp_Pnt &	P,
		gp_Vec &	V1,
		gp_Vec &	V2,
		gp_Vec &	V3
	)		const

overridevirtual

Returns the point P of parameter U, the first second and third derivatives V1 V2 and V3.

Implements Geom_Curve.

◆ Directrix1()

gp_Ax1 Geom_Hyperbola::Directrix1 ( ) const

This directrix is the line normal to the XAxis of the hyperbola in the local plane (Z = 0) at a distance d = MajorRadius / e from the center of the hyperbola, where e is the eccentricity of the hyperbola. This line is parallel to the YAxis. The intersection point between directrix1 and the XAxis is the location point of the directrix1. This point is on the positive side of the XAxis.

◆ Directrix2()

gp_Ax1 Geom_Hyperbola::Directrix2 ( ) const

This line is obtained by the symmetrical transformation of "directrix1" with respect to the YAxis of the hyperbola.

◆ DN()

gp_Vec Geom_Hyperbola::DN	(	const Standard_Real	U,
		const Standard_Integer	N
	)		const

overridevirtual

The returned vector gives the value of the derivative for the order of derivation N. Raised if N < 1.

Implements Geom_Curve.

◆ DumpJson()

virtual void Geom_Hyperbola::DumpJson	(	Standard_OStream &	theOStream,
		Standard_Integer	theDepth = `-1`
	)		const

overridevirtual

Dumps the content of me into the stream.

Reimplemented from Geom_Conic.

◆ Eccentricity()

Standard_Real Geom_Hyperbola::Eccentricity ( ) const

overridevirtual

Returns the eccentricity of the hyperbola (e > 1). If f is the distance between the location of the hyperbola and the Focus1 then the eccentricity e = f / MajorRadius. raised if MajorRadius = 0.0.

Implements Geom_Conic.

◆ FirstParameter()

Standard_Real Geom_Hyperbola::FirstParameter ( ) const

overridevirtual

Returns RealFirst from Standard.

Implements Geom_Curve.

◆ Focal()

Standard_Real Geom_Hyperbola::Focal ( ) const

Computes the focal distance. It is the distance between the two focus of the hyperbola.

◆ Focus1()

gp_Pnt Geom_Hyperbola::Focus1 ( ) const

Returns the first focus of the hyperbola. This focus is on the positive side of the XAxis of the hyperbola.

◆ Focus2()

gp_Pnt Geom_Hyperbola::Focus2 ( ) const

Returns the second focus of the hyperbola. This focus is on the negative side of the XAxis of the hyperbola.

◆ Hypr()

gp_Hypr Geom_Hyperbola::Hypr ( ) const

returns the non transient parabola from gp with the same geometric properties as <me>.

◆ IsClosed()

Standard_Boolean Geom_Hyperbola::IsClosed ( ) const

overridevirtual

Returns False.

Implements Geom_Curve.

◆ IsPeriodic()

Standard_Boolean Geom_Hyperbola::IsPeriodic ( ) const

overridevirtual

return False for an hyperbola.

Implements Geom_Curve.

◆ LastParameter()

Standard_Real Geom_Hyperbola::LastParameter ( ) const

overridevirtual

returns RealLast from Standard.

Implements Geom_Curve.

◆ MajorRadius()

Standard_Real Geom_Hyperbola::MajorRadius ( ) const

Returns the major or minor radius of this hyperbola. The major radius is also the distance between the center of the hyperbola and the apex of the main branch (located on the "X Axis" of the hyperbola).

◆ MinorRadius()

Standard_Real Geom_Hyperbola::MinorRadius ( ) const

Returns the major or minor radius of this hyperbola. The minor radius is also the distance between the center of the hyperbola and the apex of a conjugate branch (located on the "Y Axis" of the hyperbola).

◆ OtherBranch()

gp_Hypr Geom_Hyperbola::OtherBranch ( ) const

Computes the "other" branch of this hyperbola. This is the symmetrical branch with respect to the center of this hyperbola. Note: The diagram given under the class purpose indicates where the "other" branch is positioned in relation to this branch of the hyperbola.

◆ Parameter()

Standard_Real Geom_Hyperbola::Parameter ( ) const

Returns p = (e * e - 1) * MajorRadius where e is the eccentricity of the hyperbola. raised if MajorRadius = 0.0.

◆ ReversedParameter()

Standard_Real Geom_Hyperbola::ReversedParameter ( const Standard_Real U ) const

overridevirtual

Computes the parameter on the reversed hyperbola, for the point of parameter U on this hyperbola. For a hyperbola, the returned value is: -U.

Implements Geom_Conic.

◆ SetHypr()

void Geom_Hyperbola::SetHypr ( const gp_Hypr & H )

Converts the gp_Hypr hyperbola H into this hyperbola.

◆ SetMajorRadius()

void Geom_Hyperbola::SetMajorRadius ( const Standard_Real MajorRadius )

Assigns a value to the major radius of this hyperbola. Exceptions Standard_ConstructionError if:

MajorRadius is less than 0.0, or
MinorRadius is less than 0.0.Raised if MajorRadius < 0.0

◆ SetMinorRadius()

void Geom_Hyperbola::SetMinorRadius ( const Standard_Real MinorRadius )

Assigns a value to the minor radius of this hyperbola. Exceptions Standard_ConstructionError if:

MajorRadius is less than 0.0, or
MinorRadius is less than 0.0.Raised if MajorRadius < 0.0

◆ Transform()

void Geom_Hyperbola::Transform ( const gp_Trsf & T )

overridevirtual

Applies the transformation T to this hyperbola.

Implements Geom_Geometry.

The documentation for this class was generated from the following file:

Geom_Hyperbola.hxx

Public Member Functions

Additional Inherited Members

Detailed Description

Constructor & Destructor Documentation

◆ Geom_Hyperbola() [1/2]

◆ Geom_Hyperbola() [2/2]

Member Function Documentation

◆ Asymptote1()

◆ Asymptote2()

◆ ConjugateBranch1()

◆ ConjugateBranch2()

◆ Copy()

◆ D0()

◆ D1()

◆ D2()

◆ D3()

◆ Directrix1()

◆ Directrix2()

◆ DN()

◆ DumpJson()

◆ Eccentricity()

◆ FirstParameter()

◆ Focal()

◆ Focus1()

◆ Focus2()

◆ Hypr()

◆ IsClosed()

◆ IsPeriodic()

◆ LastParameter()

◆ MajorRadius()

◆ MinorRadius()

◆ OtherBranch()

◆ Parameter()

◆ ReversedParameter()

◆ SetHypr()

◆ SetMajorRadius()

◆ SetMinorRadius()

◆ Transform()